The biome with high amounts of precipitation, large narrow-leaved evergreen trees, and epiphytes including lichens is the:

Temperate rainforest biome

Explanation:

The temperate rainforest biome covers the region between 23.5° and 60° in both the hemispheres having a temperate climate. It receives a large amount of precipitation but maintains a much cooler average temperature throughout the year, in comparison to the tropical rainforest biome. It is because of its location in terms of latitude. The trees in this biome are tall and green and are comprised of narrow leaves. The epiphytes are a dominant species here and are frequently a species of both mosses and ferns, and they mostly dwell on the tree trunks as well as on the branches. Lichens are also found to be associated with these epiphytes.